Constraints on Warm Dark Matter from Cosmological Reionization

We study the constraints that high-redshift structure formation in theuniverse places on warm dark matter (WDM) dominated cosmological models. Wemodify the extended Press-Schechter formalism to derive the halo mass functionin WDM models. We show that our predictions agree with recent numericalsimulations at low redshift over the halo masses of interest. Applying ourmodel to galaxy formation at high redshift, we find that the loss of power onsmall scales, together with the delayed collapse of low-mass objects, resultsin strong limits on the root-mean-square velocity dispersion v_rms of the WDMparticles at z=0. For fermions decoupling while relativistic, these limits areequivalent to constraints on the mass m_X of the particles. The presence of a 4billion solar mass black hole at z=5.8, believed to power the quasar SDSS1044-1215, implies m_X > 0.5 keV (or v_rms < 0.10 km/s), assuming that thequasar is unlensed and radiating at or below the Eddington limit. Reionizationby z=5.8 also implies a limit on m_X. If high-redshift galaxies produceionizing photons with an efficiency similar to their z=3 counterparts, we findm_X > 1.2 keV (or v_rms < 0.03 km/s). However, given the uncertainties incurrent measurements from the proximity effect of the ionizing background atredshift 3, values of m_X as low as 0.75 keV (v_rms = 0.06 km/s) are not ruledout. The limit weakens further if, instead, the ionizing-photon productionefficiency is greater at high z, but this limit will tighten considerably ifreionization is shown in the future to have occurred at higher redshifts. WDMmodels with m_X < 1 keV (v_rms > 0.04 km/s) produce a low-luminosity cutoff inthe high-redshift galaxy luminosity function which is directly detectable withthe Next Generation Space Telescope (abridged).Comment: 38 pages, 10 figures, to appear in ApJ. One figure added, some discussion revise